{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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42mnzHdOaqPCw1hITE1PochMTExk/fjyNXnqJtm3bsHTpUnJych547tdff4VB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TAAAg\nAElEQVRy/Phx/Pz8gLRifO7cOQ4dOvTBxfcfxsbGtG3blq1L5nFy7zZSkpOJuH6ZX0f1w9a2AE2b\nNn1jm507d7Ji+XJ6jJ/FT6t28uNva/h59S5uhoczadKk97YZGxvL6DFjqO/XiR8WrOKrLn0YNm8F\nvv7fMW78+AydIKWcp1GjRoSGhlKgQAG8vLyYPXv2Z9+ekqR3ydLiryhKK+AXYAzgCpwD9iiKYpWV\n7Upv17p1ax5F3mHXqsXpHyw3L4RydPt62rTJ/Fntrl69ioGREU5lXDIsL12pKnGvXhIT9ZTYF9H8\n8fMPoCgkxL3Go24jJq7eRaXavjy5f5e4Vy9ZExBAdHQ0awICsLJ6959OcnIyERERvHr1iho1arB+\n3TrCQkNYExBAlSpVALh8+TIuLq64uLhQu3Zt7OztGTly5Ed92M6aNQvvGmmzC7b3cGT4/7V332FZ\nVm8Ax7/nfWWDLMUFbs2JgnvhwpV7oWZuc880zZE5M1euUjP3AFfuUW7NPVA0U8vc5kQBRRGB+/cH\nyi9yoi+8CudzXc9VHJ7nPPcReO9nnNG0Go9D77Jhw3qsra2f23/FihV45MhN2ZoN4soy58pL2Y8b\nsHDhotee7+DBg4Q/eIBv45bxyqs0bsmjhw85cODAG8euvZ8yZ87Mrl276N69O7169aJRo0b6ok5L\nNIl9598b+FFEFojIGaAT8BBom8jn1V7Ax8eHXr16sei74fSpW46vPq3JkFZ1KJi/AAMGDHjpcZGR\nkYwfP578BQqSIWMmGjVuzLFjx157vuzZs/MoPJzLf56OV/5X0FGUwcDXrevRpao3gbu3ITEx/BIw\nmwmft+PG5QtYWdtw88pFWrZqhZ+f32vntxcRJkyYQCZ3d7JmzYqrqytt2rQhNDQ03n7h4eH4+lYh\n5OFj+k1dwLifd1D9k/aMGjUqQY/P7e3t2bhxI4GBgfz000+sX7+e8+f/fm58/jMPHz7Ewsr6uQ5d\n1rZ23Am+wx9//PHK8z3rPxAeFj8ZPHj69X/7F2gfJktLSyZMmMDq1avZvn073t7eHD161NxhacnR\n64YDvO0GWABPgDr/KZ8HrHrJMXqoXyKLiYmRXbt2SefOnaVly5aycOFCiYiIeOX+devWE2OqVFKm\nRn2p1667ZMyaXaytrWXfvn2vPNfjx48lS5as4pEjtwz6calM3xIobQd+IxaWVlKiRAkBJHs+T/ny\nh0UyaMYS+ahwMTEYjQJIakdH6d+/vzx+/PiN2jV27FgBpHLDT6Xf1AXSrMdAsXNILRUqVIybEVBE\nZPbs2aKUkolr98QbMle+jp9kyuQeb19TiIiIkEWLFkn+/PljZyj8akzcOWdsOy6pXdKIhaWVWFhY\nyIYNG15aT1RUlGTOnEXyFS0ls3b/If6BV2T2b6elQPGykimTu14+Nhk6f/68FCtWTCwtLeX77783\n+e+mlvy8F0v6AhmAGKDEf8rHAPtfcoxO/u+ZnTt3CiA9xkyPS1rz9v8l2fIWlPLlK7z2+NOnT0u+\nfPnjptpVSknzTz+VSpUqSS5P77ilbJ8lM/vUjtKzZ0+JjIwUEZFdu3ZJg4YNpaCnpzRs1Eh2794t\nIiI3btyQgIAAWbVqlQQHB4trmjTi27hFvITeZ+IcAWTv3r1x8fTr10/SuWd+bvrdLiMmCyAPHjww\n2b9dSEiIFClSVADJkjufOLqmFUA8cuWVas3aiqNrWkntkkbGr9whhctUlIwZM70yie/cuVNs7ezE\n1s5e8hUpKbb2DmJjaytbt241Wcza+yUiIkK6d+8eu/Szn59e3ll7pQ9+nH/v3r2fG7fcrFkzmjUz\n/Xtp7dU2b96Mcxo3SvjWjCuztLKmUv1PmP3NAB4/foyVldVLj8+TJw+//36SAwcOcOPGDQoXLky2\nbNnI5O5B8RoN4j0Gt7GzJ0cBLy5duoSFhQXz58+nTZs2eOT4iNxexTh87DA+Pj7Uq1ePDRs2xM3U\nZ+/gwIP79yle6eN45/YqVxkLC0uOHj0aN7Vujhw5uHP9GsE3/sE1fca4fc8GHSZduvQmfXw+fPhw\nTp85w4iF68iRvzAx0dGsnjOVFdMnEHb3NsUq1aB2qy6kzehOgw69GdKqDgcOHKBs2bIvrK98+fKc\nOX2aWbNm8ddff9Hw4yq0b9+ezJkzmyxm7f1iZWXFlClT8PHxoV27dhQtWpTly5dTqFCh1x+sJWsB\nAQEEBATEK/vva85XSczkfweIBtL9pzwd8MpZWiZOnPjSd6da0rK2tibycQRRTyKxsPx/kn/44D4W\nFhZv1PNeKfXc8r/Zs2Xj75Px+w08iXzM5bOnqFi8OQ8fPqRX796UqVGfTsMnxo7Vj4lheLuGrF69\nmnrtulOtWVsiwh+w5PsxHNq6gVNH9lGgxP8T582rl3jyJJL06dMDcO3aNdKmTYu9gwOTvujAp32+\nxi2TB3s2rGLHSn9GjBhh0klWFi/2p3y9pnEdHg1GI/XadmfL0vkUKl2RtgO+idvX0iq2k+Drph72\n8PBg2LBhJotR+zA0atSIwoUL07hxY0qUKMHUqVNp3769nhQoBXvRDXFgYOBr50F5JtE6/InIE+Ao\nUPlZmYr9Ta0M7Eus82qm1bhxY8Lvh7Hqp8lxC5Hc/ucKm5fOpX6DBm89e1337t04efA3/CeN4u6t\n61y7cI7vB3TjQVgIHTt2ZN++fYTcu0edNl3iZh00GAw8jnhEgRLl8OvaD0eXNKTzyErXkZNxcHJm\n06KZ/H5wDyLCzSsXmTm0D2nd3GIn02nThsyZM9OgQQNCQ0L458I5hrVtQNdqxVg+bSxdunShf//+\nJvt3A3gQ/gBHl/ijEwxGI/aOzvx1MjBudIGIsHHxTJycneNGJGjaf+XMmZP9+/fTpk0bOnToQIsW\nLXjw4IG5w9I+VK97L/AuG+BHbO/+lkAe4EcgGEj7kv31O38zu3LligQFBcmjR4/iykaOHCmApHeP\n7XCWysJCsmTJKpcvX36nc40aNUqsrKzi+gM4u7jIypUrJSIiQtq3by8GYypxdE0rpWvUk7HLt4p/\n4BVxdEkj9T/r+dw7e89S5cXZ2Tl2Pn07OwEkTdq0sm/fPunUqZNYWllLq37DZeLaPdJr3ExJkz6j\n5MqVW1auXCnXrl17x3+1F6tdu464Z88l8/b9GRfnsHlr4tqbLW8ByeNdXOwdY+P+9ttvEyUOLfnx\n9/cXe3t7yZMnj5w8edLc4Wjvifeiw5/8P6F3AS4Cj4D9QNFX7KuTv5lcvHhRKleuHJeYXFxd5bvv\nvovrYbx3717p0KGDNGrUSL777juTLSRz584dWbFihaxfv14ePnwo0dHRUr16DUllYSFlatSX2q27\nSNpMHmJlYysjFq4XR9e0kj2fZ7yOgrN2nRJbewcZOHCgbN26VcaNGyeLFy+W8PBwuXfvnlhZWUmT\nbv3jXSwMnrlMANmxY4dJ2vEiR48eFRsbG3HPnkv8uvaT6s3aiY2dnRQrVlwmTpwollZWksrCUnIW\n9BJbewexsrKSdevWJVo8WvJy5swZKViwoNjY2MjcuXPNHY72Hnivkn9CNp38zSMiIkKyZ88hbpk8\npMuIyTJk9s/i27iFAK9dQc/UNm7cKID0nTQ3LlHP2XtWMmbNIVY2tmIwGASQklVry9C5q6T/1AWS\ny9Nb7B0cXvgk4uTJkwLI0Lmr4iX/RUcuJUn7jh49KrVr1xF7BwfJkCGj9O3bV0JCQqRQocKSLU8B\nmb71WFwbi/j4irOLizx8+DBB57h27ZoMHDhQKlSsKA0bNZINGzboYWEpRHh4uLRr104Aad26tYSH\nh5s7JM2MEpL89dz+Gj///DPnz/9N30lzKVuzAXm8itN2wDeUqlaHb78dE/duOils3ryZdJk88CoX\n11UEaxtbKjb4hCePI9i2bRt58uTh0LaNDG1TnzHdW3LxzCkmjB+Ph4fHc/VlypQJS0tLzh47HK/8\nz6AjQGzv/8Tk7e3N2rVruB8Wxj//XGPcuHFcv36doKDjNOzUJ65PgLWNLZ/0/op7d++yefPmN67/\n7NmzFCpcmElTpvLQaMuxU2epWbPmKydt0pIPW1tbZs2axfz581m2bBnFixfn9OnTrz9QS/F08k+G\noqKiWLlyJd26dePLL78kKCjolfufPHkSt4zuuOf4KF65V9nKXLhwnocPHyZmuPFYWlryMPwBMdHR\n8cojwsMxGI3MnTuXq/9cp9fYHxmxcD1fTJ5H9nyeDBo8+IVxOjs707JlS1b9NIltPy8m+MY1Zgzt\nw+jOn6CUok/fvixdujSpmgfEzjIIYO/oHK/cwck53vffRJ8+fbGwseO7NXvoNXYGIxdvpGmPAYwZ\nM4ZTp069vgItWWjZsiWHDx8mJiaGYsWKsWjR66eM1lK293Kcv/Zqjx49wt/fn+3bt2NnZ8cnn3xC\n+fLlUUpx//59qlevwb59e3HPlpMHYSGMGTOGkSNHMmjQoBfW5+7uzt3bNwkNvo2ja9q48gtnTuLs\n4oKNjU1SNY1s2bJxP+QeGxb+SO3WXVBKcePyBTYvm0d0VBQBS5bQuMsXFK1YLe6YjFlz0LtuOdas\nWfPCuSAmT57MgwfhzPlmACKCUopytRqRLa8nQXu307RpU+7du0enTp2SpI0FChQgTZq0bF+5iFye\n3nHDtbb9vBij0YiPj88b1RMREcHGjRto+cUwwsNCWDJ1NGcCD2JjZ4+llTXLly8nf/78idkU7T2S\nL18+Dh8+TOfOnWnRogW7d+9m8uTJSfr3q31AXvdeICk39Dv/17p7964UKlRYlFKSy9NbMmTOJoD0\n6tVLRET69+8v1ra28tVPy8U/8IosOHhe6rXvIYAcOXLkhXUGBweLja2t5PEuKeNX7pT5B85JhyHj\nxJgqlfTu3TspmyezZ8+O63SYIWsOyVe0tBhTpRLXdBnjyvtPXRDv/f3io5fF2tZWxo8f/8q6d+zY\nIUopafnFsHjH+tRuLGnd3N54KmFTmDlzpgBSoHgZadZjoJTwrSmA9OnT543rePjwoQBSv31PsbF3\nEBe39FKtWVspVrmGKINB8uTJq9/9v8C9e/dk2LBhUqRoUSlevLiMHj1a7t+/b+6wTCYmJkZmzZol\n1tbWUqhQITl79qy5Q9KSiH7nn4yNGDGCv/7+m1H+mxg2bw3jV+3i08+HMGnSJPbs2cPChYsoX7cp\neYvEjhdPZWFBo46f4+qWnsWLF7+wzsePH/MkMpLzfxynb4MKtCqZk5nDv8BgMHL37t2kbB558+YF\noGmPAeT2LIJdakc+6TUYnzqNsbKyIk2atBzZtZmY6Gg2LJpJnwYVaFPmIyIjIoiMjHxl3RcvXkRE\nqFCvaVyZUooK9Zpy+9at596Vnj17lnbt2pEnbz5Kly7DTz/9RPR/Xke8rc8++4yVK1dib4hh/bzv\nuX/9EtOnT2fcuHFvXIeNjQ2VKlfm1yVzcHJ1Y9zPO2j1xTB6j5tJj2+ncebMabZv326SeJOLkJAQ\nypQpyzejv8UqrTsGRze+/nooFSpUTNDrlveZUop27dpx8OBBHj16RNGiRVm2bJm5w9LeMzr5f2CW\nLFlK+Tp+ZP0o9nGuUorqn7TDLZMHS5YsIex+GM5p3OIdYzAaSe2ShrCwsJfUuQSDMRWT1+6j94Sf\n+GzIOMat2E699t1ZunTpK2ede/DgAXfv3jVZp8CSJUtSqlRpfln8E3mLlKRRp8+Jioxk/fzptG/f\nni+/7M+2FYvo5+eL/6RRZM/rScOOn5OzoDcDBw6kfPny7Nmz54V1P1sZMPTOrXjlIU+//vfKgceP\nH6dosWKs2bCJzJ7FeWxhS8eOHWnVurXJ2lq/fn32799HWGgop34/SadOnRI8Y9vYMWN4FP6ASg0/\nwcbOPq68eOWPSZshExs3bjRJrMnFlClTOH/hAiMXb6TbqKn0GDOdofNWczzoOLNnzzZ3eCbl6enJ\nkSNHqFmzJk2aNKFr1648fvzY3GFp7wmd/D8wDx89xC61U7wyg8GAnUNqHj16hE85H/ZtWk3k44i4\n7184fZILZ36nfPnyL6zz7t272DmkJrVrGopVrE7Fek3JlD0XaTN4EBERQURExHPHXLp0iXr16uPo\n6IirqyuFC3vxyy+/vHP7lFKsWbOaUsWLMePrz+nvV4UV08fRtk0bvvvuOz7//HP69u3LPxfO0br/\nCLqOmkLtVp34es5KilWszv4DBylXrhwTJkx4ru7q1avj7OLCgvFDeXg/9kLozvVrLJ82jvwFCpAt\nW7a4ffv3/xJnt4yM+3kHbb4cSd9Jc+k4dAKLFy3iwIED79xOU/H29sbSyoon//kZSUxM7JTMFhZm\niuz9tGbtOrwrVCVTtpxxZVnzFMCzZHnWrF1rxsgSh4ODA/7+/kyfPp1Zs2ZRunRpzp8/b+6wtPeA\nTv5J4OTJkyxbtoxDhw69811jlSpV2LPhZx6F/39azz+DjnDhzCl8fX0ZOvRrbl29yNet6rBh0UwC\npoxmdOdmFCoUOy/4i5QpU4Z7d25x6tDeuDIRYe+mVRQoUBB7e/t4+4eFhVG+fAX2HTpMi75D6fbN\nVKKt7KhVqxa7du16p/YBpE2blo0bN3LhwgX27NnDtWvXmDFjBpaWliilyJ49OwajkQp1m8Qdo5Si\nUsPmPIl8TLFKNejXrx9XrlyJV6+trS2LFy3i94O/0bmqN/39fOlVuzS3r1/l1O+/U6NGDa5evUpk\nZCRbtmymcqNPsba1izu+bM2GOLmmYf369e/cRlNRStG4USO2rljInevXgNif3S8Bc7h35zaNGjUy\nc4TvF6NBPTeSBCAmJgqDSp4fh0opOnXqxP79+wkJCcHLy4uVK1eaOyzN3F7XKSApN5JZh7+7d+9K\nlSpV4jqqAVK0aDG5cuXKW9f5+++/i0Pq1JIuU2ap176HVG74qVjb2ErJkqXiOqwdOHBAqlatJhYW\nFuLk7Cxdu3aV4ODgl9YZHR0tpUuXEVt7B6nXrrt0+Hq8FCxZTgBZuXLlc/tPnTpVjEajTFy7J67j\n3MJDFyR73oJSpUrVt27bm5o/f74A8sOvR164LG+O/IXEwsJSpkyZ8tyxd+7cEUtLS8lduKhUbvSp\ntO4/QmbuPCnFfWuKMZWFuKVLJ3/99ZcYjUZp/vlX8epfcPC82DqkloEDByZ6GxPi8uXL4uGRWSyt\nrKVw2UqS9aN88TqBav/3zTffiKWllXzjvynu5/r1nJViMBhk2rRp5g4v0YWEhEjDhg0FkJ49eyZp\nJ1ct8ekZ/t4T9erVFwdHZ+kxZrrM3HlS+k9dIGkzZJKiRYu9Uy/sU6dOSdNmzcTNLZ1kzZZdBg0a\n9M69lUNDQ6Vr165iZ28vgHh6FpJVq1a9cN8WLVpILk/v5+bXb9Ktvzg6Ob1THC8TGRkpq1evlsmT\nJ8uaNWvEyspaSlatHTdv/tRNhyRD1hySMVtOAcTSyvqFvf+XL1/+9MLhcLzYh85dLYCkdnaV1q1b\nS8WKFcUlXQaZtvlo3KiAZj0HCSDdunVLlDa+i+DgYBk9erRUr1FDmjVrJhs3btQ9/V/g/v37UqRI\nUTGmSiXe5XylUOkKYjAYpFw5n3jrWSRnMTExMmXKFLGwsJDixYvLhQsXzB2SZiI6+b8HLl++LEop\n+WzIuHhJpv/3CwWQAwcOmDvEF4qOjn7th+Dnn38uTq5pZcHB8/Ha5lO7seTImcvkMZ08eVIyZ84i\ngFhYWAogrq6uglJil9pRchbwEmMqC3FK4ybtvxob95Tl1KlTz9W1enVskp+45rd4sQ+cHiCAVKjb\nRFxd00iLFi0klYWFWNnYStGK1SRrngICiHuOjxKljVrSefDggUyaNEkqVa4svr5VZNq0aSkm8f/b\noUOHJGvWrOLk5CRr1qwxdziaCeihfu+By5cvIyLkKugVrzxXQW8gdtjZ+8hgMGBtbf3KfVq3bk3o\n3TssGP81Dx/cJyY6mn2/rGbvplW0b9fWpPFER0dTt249lLUt3y7dzLwD5xg8cxlPogVEyJG/MBmz\n5eCTXoMYu3wrQXu2YzAayZ49OwMGDGDatGnxZv7z9fUltaMjy6aNIzoqCoDHjx6xevYU0nlkxS61\nE0ajkejoaNwyepDOPQtnjx3mSeRjuoycTAnfmtxL4uGPmmnZ2dnRs2dPtm3dypYtm+ncufNrf+eT\no2LFihEYGEj58uWpW7cuX3zxxStH9mjJzOuuDpJyIxnd+V+/fl2MRqO06Ds03h1mr3E/CiBBQUFm\ni+3x48eyatUqmTJliuzYseOtHg9Pnz5djEajWFhaiX1qRwGkQcOGEhkZadJYt2zZIoAMX7A23r9j\nh6/HCyAGg0FKV68nzXoOklyeReLu+nMWKCz5i5cRg8EghQt7xVuF0N/fXwwGgzilcZOiFauJg5OL\nWFpbS9dRUyS1s4t07txZateuLYBkzJZTilSoKjZ29uLg5CLpPbJKrVq1TdpGTTOnmJgYmTBhgqRK\nlUpKly79zkt1a+ajH/u/J1q1bi3WNrbSou9QGbtim3QYMk5SO7lI5cqVzRZTUFCQuLt7xHuEXqxY\ncbl169Yrj4uOjpbff/9d/vjjj7iLhStXrsjEiRNl1KhRsn///kR5x/ysc9+zd/vPtpGLNgggvXv3\nlly5PxJ7BwfJmy+2o1uPMdPj9vsm4BextrWVwYMHx6s3MDBQcuaM7R/gnDad5C9eViytrCV79hxy\n4MABUUpJ3bbd4pYOnrEtSNJnziZGo1EOHjxo8nYmR48fP5bg4GDd9+ADsW/fPvHw8BBXV1fZuHGj\nucPR3oJ+7P+emD5tGk2a+OE/cQT9GlVm5vAvKF+urNlm24qKiqJOnbqkskvNmGVbmHfgHAOnB/DX\n+fO0b//ZS4/btGkTuXLlpkCBAuTLl488efKyfft23N3d6dWrFwMHDqRkyZIJnqDmTRQuXBiAI7vi\nr3R3ZOev2NjYUqtWLbZs/pX7YWEU8vQkez5PSlapFbdf1o/yU6paXZYuWx7veC8vL86ePUtAQABl\nS5UgnYMVQ78ewuHDh9izZw+WVtbUa9cjrk2pnV2o1bIT0dHR5MmTx+TtTE7CwsLo2LEjTk5OuLq6\nkiNHTubPn2/usLTXKFWqFMeOHaNEiRJ8/PHHDBw4kKinr8a05Ecv7JOIbGxsmDd3Lt+OHs25c+fI\nnDkzmTNnNls8W7du5dKli4xavBGPnLEJrECJsjTq/AWzR33J9evXyZAhQ7xjjh07Rt26dclbtBQD\n+g4nJjqadfOnU7NmTQIDA+Om400snp6e1KxZizkjv+TO9WvkyFeIoH072bBoJkaDgcqVY5f+9fX1\nxdLSEkur5xcxsbK2feHUvwaDgaZNm9K0adN45VFRURiMBoyp4v95WFhaxX1fezERoXbtOhwJDKRm\nqy5kzJqDg1s30Lp1a6Kjo2nb1rR9QjTTcnV1Zd26dYwbN45Bgwaxd+9eAgICyJgxo7lD00xM3/kn\ngfTp01O2bFmzJn6Af/75BwCPnPGX7s2cKy8iws2bN587ZuLEibimy0jfSfMoWNKHQmUq0m/qAmxT\nOzFlypQkiXvJkgCaNvFj5YwJjOrUlK3L5iMxMeQvUY7OwyfRecRkjp08RVDQCc4eP8S534/FHRty\n5xZ7N62kahXfNz5fjRo1eBQezvaV/18LIfJxBFuWzaNkyVK4uLiYtH3Jyc6dO9m9exfdRv9Agw69\nKFm1Nj3HzqBU1doMGzacmJgYc4eovYbBYKB///7s2LGDc+fOUbhwYbZu3WrusDQT08k/BfHyih15\ncHTXlnjlR3b+ip29PTly5HjumKATJ8hfohyp/jVNrKWVNfmKlubEiZOJG/BT9vb2zJ49m9u3b7Nm\nzRqeRMX2SA7au4PpQ3qxa80S2n81lmvXrpIrd26Gt2vE9CG9mfvtYL5oVJnw+2Hs3v0bISEhb3Q+\nT09POnbsyLwxXzG2e0sWjBtK/8aVuXruDOPHv/nCOynRwYMHsXNITaHSFeKVl6xWh8uXL73wAlN7\nP5UrV45jx47h5eVF1apVGTp0qMkWttLMTyf/FMTLy4tq1arx0/AvWDd/BqcO7WXxxBGsnz+dnj16\n4ODg8NwxWTJn4eKZk886ZAKxj3YvnjmJR2aPpAwfOzs7evToiZt7FkYsXMfCQxfoM3EOl/86zc7V\nS7Cxs6NA/vxEPYnk7LFDnDywm7I1G/DlD4u4dOUy33333Rufa9q0acydOxc7nnDuyG6qVizPwYMH\nKVOmTCK28MOXNm1aHoU/IDT4drzym1cuYmFhEW/xJO395+bmxqZNmxg+fDgjRoygatWq3Lhxw9xh\naabwuh6BSbmRzHr7v4/CwsKkdevWYmkZ29M/taOjDBkyRKKiol64/6ZNmwSQjz/9TGZsC5LpWwKl\nSuOWAsiuXbuSNPZffvlFABmxcF28nv9tvhwpymB4OnKhmOT1LvHc7IM+tRtLvvz5kzTelOjevXti\nZ28v3j6+Mn3rMfEPvCJDZq2Q1E4u8umnn5o7PO0dbN++XdKlSyfp06eX7du3mzsc7QUS0ttfd/hL\nYRwcHJg7dy6TJk3i1q1buLu7Y2PzfCe5Z6pXrx7X+Wfjop8AsLa25vvvv8fHxyepwgbg6tWrAGT9\nqEC88qx5CiIxMbi5uZE2bVoe3n7+8b4xVSpiYkyzFK/2ck5OTixftoxGjRvTrXoxUjs5c+/ObYoU\nKcqkSZPMHZ72DipWrMjx48f55JNP8PX1ZdiwYQwcOBCDQT9A/hDp5J9COTo64ujo+Eb79u3bl1at\nWrF582aUUlSrVg1XV9dEjvB5BQsWBODYnm0UrVAtrvz43thZ/VavXs3vv/9Ox44d+TPoKLkLFQHg\n5tVLHNyynh7duiZ5zClRjRo1uHL5MkuXLuXmzZsUK1aM6tWrYzQazR2a9o7Sp0/Pli1bGD58OEOG\nDOG3335j0aJFpE2b1tyhaQmkRN6fuyGllDdw9OjRo3h7e5s7HO09IyJUqlSZo4mN4OgAABlZSURB\nVMeO07DT52TL68mxPdtYO/cHevfqxfjx44mIiKByZV8OHT6Et08VLK2sObLzF9wzZmL//n2kSZPG\nLLFfv36dgIAA7t69S5kyZahWrZq+Y9I+aFu2bKF58+ZYWlqyZMkSypYta+6QUrzAwECKFCkCUERE\nAl+58+veCyTlhn7n/0G6dOmSTJgwQUaMGCF79+5N1Bnd7t69K439/MTw9B2/rZ2dfPHFF/LkyZO4\nfcLDw2X8+PFSokRJ8fYuIkOGDJE7d+4kWkyv4+/vL5aWlmJpZS0uadMJIKVLl5HQ0FCzxaRppnDt\n2jUpV66cGI1G+fbbbyU6OtrcIaVoenpfLcn88MMPYjQaxdLKWuwdnQSQ+vUbJPo64Tdv3pTjx49L\nWFhYop7nXV29elUsLCykTI36MmvXKVl89LIMmrFEbO0dpEuXLuYOT9Pe2ZMnT2TAgAECSM2aNc16\noZ3S6el9tSRx4sQJunbtSqWGnzJ96zFmbAui++gfWLd+HRMmTEjUc7u5uVGoUKEXDk80hRMnTtCt\nWzfq1q3L4MGDuXLlylvV4+/vjzGVBW0GjMLWITVKKfIXL0PVpm2Yv2CBHjetffBSpUrFN998w4YN\nG9i/fz9eXl4cOHDA3GFpr6GTv/bW5s+fj3MaN1r2HYqNnT0Gg4FS1epQpkZ9Zs+Za+7w3tqiRYvw\n8vJiyYqVXAq+z8TJU8hfoACHDh1KcF3BwcE4ODljax//IiWdexbCHzx44bTD7yoyMpJ79+49e5qm\naUni448/5vjx47i7u1OuXDkmTpyofwffYzr5a2/t9u3bpM3o/twc+Ok8snLnzu2XHJV4bt26xZgx\nY2jTpg0jRoyIGxqYEKGhoXTs1InSNeozce1e+k9dwOQN+3HzyMZnn3VI8IdZqVKluH39GmePH44r\nExH2/7oGT89CrxxmmVD379+nU6dOODk74+LiQs6cuViwYIHJ6te01/Hw8GDXrl307NmTzz//nAYN\nGnDv3j1zh6W9gE7+2lsrUaIEf58K4ubVS3Fl0VFRHN62kRLFS7xT3TExMfzyyy90796dnj17smvX\nrlcm3sOHD5P7o48Y8vVQ9h4NYvSYMeT+6CO2bduWoPNu2rSJh+HhNO3eP25KYzsHR+q178GJE0Gc\nO3cuQfXVrFmTokWLMaF3W1b+NInf1v/M2O4tOLF/N8OGDU1QXa8iItSqVZuFi/35uEUnuo/+gTTZ\nPqJVq1bMnfvhPoXRPjwWFhaMHz+eNWvWsHPnTry9vTly5Ii5w9L+63WdApJyQ3f4+6CEhYVJ1qzZ\nJE36jNKi71DpMmKy5CtSUoxGo+zevfut642MjJR69eoLIOk9sopbRncBpG3bti/sTRwTEyN58uSV\nHPkLyYxtQeIfeEVm7TolBUuUk3Tp00tkZOQbn3vevHkCyKxdp+LNEDhoxhIB5OTJkwluz927d6V1\n69aSKlUqMTztHFmseHHZv39/gut6me3btwsg/acuiBd3ySq1JEuWrLoXtmYWFy5ckGLFiomFhYVM\nmTIlUUcCae9Jhz+l1ECl1F6lVLhS6m5inUczHwcHB3bt2olPmVL4TxzBtK96YhUTycaNGylXrtxb\n1ztr1izWrl1Dr3EzmbB6NxPX7eOzIeOYM2cOK1eufG7/oKAgzpw5jV/XfqR2jl1xz9YhNc16DeLm\njRvs3Lnzjc/t6+uL0Wjkl4A5cWUxMTH8unQuHh6Z32oJY2dnZwCio6MpVrE6H7fowI3gUHx8fEy2\nWtqzBXU8/7OgTqlqdbh06SK3bt0yyXk0LSGyZs3Knj176Ny5Mz169MDPz4/Q0FBzh6WRuDP8WQDL\ngP2AXsQ7mcqcOTM/r1jBw4cPiYyMxMnJ6Z3rXLRoMV7lKlO8co24sor1mrJzdQCLFi+mUaNG8fZ/\n8OABAKld4k/g4+jiGvf9mJgYtm/fzt69e3FxccHPz4906dI9d+5MmTLRv39/vvnmG/46cYSseQpy\nYt9OLp49xdKlS99qlrrjx48zb9482g8eQ6UGnwDQ4LNejO7cjL59v+DYsUCUUgmu999cXV2JeBhO\naPBtnNK4xZXfvHoJCwuLRBsVoWmvY2lpyeTJk/Hx8aFt27YUKVKE5cuXx60yqplHot35i8gwEZkM\nJM26r5pZ2dramiTxA4SGheLo6vZcuZOrG2FhYc+Ve3l5kdrRke0/L45Xvu1nfywsLChcuDCVKlWm\nSpUqTJw8hT59+pIlSxaWL1/+wvOPHDmSRYsWYUcURzavIW/2LGzbto3GjRu/VXs2b96MjZ0d5ev4\nxZWlsrCgcuMWBAUd586dO29V7781atQIaxsbZo/sT9i9YADOHDvE+nnT8WvSBDs7u3c+h6a9i4YN\nGxIYGIijoyOlSpVixowZejSAGem5/bX3TqWKFVmw2J8m3frj4BT7yDz4xj+c2L+LQQMHPLe/nZ0d\nw4YOpXfv3ty5fpV8xcvwV9BRDm3byMCBA5k4cSKHjhym//cL8SxVnvCwEOZ+O5hPP/2U0qVLkylT\npnj1KaVo3rw5zZs3N0l7rK2tiXoSReTjCGxS2ceVP3r6xMLS0jJB9QUHBzN9+nQ2b96Cra0tzZo1\npXnz5ixbupTGTxfUcXB04t6d23h7F2GyXlBHe0/kyJGDvXv30qdPHzp37szu3bv58ccf9ZMpc3hd\np4B33YBWwN033Fd3+NPk4sWL4pomjbhl8hC/Ll9Igw69xTmNm3h4ZJbbt2+/9Dh/f3/x9i4itnZ2\nkj9/Afnxxx8lKipK7B0cpE6brvE6ws3adUqsrG1k7Nixid6eK1euiNFolGrN2sqiwxfFP/CK/PDr\nEcmQOatUq1Y9QXVdv35dsmXLLtY2tlLct6YUKF5GAGnQoKFER0fLnTt35IcffpAhQ4bI+vXrX7pU\ns6aZ25IlS8Te3l7Kli2rOwKaSKIt6auUGg30f9W1BJBXRP58mwuRZ3r37v3cinPNmjWjWbNm71Kt\n9oHIkiUL+/bu5ashQ1g/fxpGo5EG9eszcuTIVy7M86LfkYiICB7cv0/6zNnilds6pMbJNQ23byf+\nfATu7u5MnDiRHj16cGzXZtzcs/Jn0BGcnZ2YMmVyguoaOXIkwfdCGLN8K2kzegBwaNsmJn3RgfXr\n11OnTh26dOmSGM3QNJNq0qQJXl5e3Lx58537vKREAQEBBAQExCtLSGfKBK3qp5RyBV63lut5EYn6\n1zGtgIki4vIG9etV/TST8/QshMHBmX5TF8Z9yJw7eYwhrerw888/06BBAyD2D+enn35iy5at2Nja\n0KxpUxo3bmyy1feOHDnCnDlz4pa5bd++fYJXGcyUyR2vyjVp3vureOUDmlSlYpkSeky/pqVgCVnV\nL0F3/iISDAS/Q2yaluSGDv2ahg0bMr5nG8rUrM+df66ycdFMChUqTO3atYHY2QrLli3HhQsXKFCi\nHOE3rtC0aVPWrF3LooULTXIBULRoUYoWLfpOdcTExGAwPD/iwGA06M5Tmqa9scQc5++hlCoEZAGM\nSqlCTzfd7VhLUg0aNGDZsmU8vH2N7wd0Y+WP31G3Vk22bt2CxdNZ/EaOHMk/N2/y7fKtfDFlHkPn\nrabrqCkE+PuzadMmM7fg/+rUqc1v65dz7/aNuLLje3dw4cwp6tSpY8bINE37kCTosX+CKlZqLtDy\nBd+qKCK7X3KMfuyvJRoR4d69e9ja2mJtbR3ve5kyuVOoYg1a9Pk63v5f+vlSsUxJpk2b9sLhciLC\nwYMHWblyJdHR0dSqVYsKFSok2jvMq1evUrJkKe6FhlKkQjXCw0I4vmc71apVZ926tW81D4GmaclD\nQh77J+Y4/zYiYnzB9sLEr2mJTSmFi4vLc4kfYmffs7C0ild269pl7t66wcKFC7G3t6dcOR/2798f\n930RoUuXLpQqVYrZ8xaw0H8JlSpVommzZom2VK+7uztHjhymR7euPPjnArYxj5k6dSqrV6/SiV/T\ntDemF/bRUozHjx/z7bffki9ffjJkzESTpk05ceIEADVrfsye9SsIDY7t/R927y5DWtXFysaWT/t8\nzWdfjeWfu6FUqlSJoKAgAFatWsWMGTNoM2AUUzYdYtKGA3T7ZirLly1jzpw5L43jXaVPn57Ro0cT\nePQIv/22my5duiR4rgBN01K2RHvs/zb0Y38tscTExFCrVm22bN1Cyap1cE2XgYNb1hMafIvdu3aR\nJk0aSpYqxaOISIpV/pizQUe4celvJq3bi4tbBgAiH0cwoElVypcpSYC/P/Xq1+ePvy8xbP7aeOca\n16MVdjzht9/0Qy5N05LOe/HYX9PeJ1u2bGHTpo30HPsjXUZMokm3/oxespm0mbIwaNBgsmbNypHD\nh2nTqgX/nD7Ggzs3yFe0dFziB7C0sqZACR82bNhAocJe7Ny5k0ePHhIZ8SjeuZzdMhASGpLUTdQ0\nTXtjOvlrKcLmzZtxy+iOt49vXJmVjQ0V6jVl69YtxMTE4O7uzqRJk/jj1O/Ur1+fO9evxBs+F3Ln\nFr9tWMGTJ1E4Zc5FnqJl+OfCOUZ0aMKTyMcAPAgLIXDXr5T38UnyNmqapr0pPbe/liJYW1sT8egh\n0VFRpHo6vA/g4YMwrKysnuud37p1a+bOncvy6eOp1647qVJZMH1Ib5TBwJilW0iTIXY9gDPHDjG8\nXUO+H9idnAW92bnKHyUx9OnTJ0nbp2malhD6zl9LEfz8/Ai7d5d186fF3c3fuHyBrcsW4Ofn91zy\n9/HxYcSIEayeNYUuvl50qeLNH0f2UfbjBnGJHyCPV3FyFyrK0Z2/smLaWEoUKczePXvIli3+dMKa\npmnvE33nr6UIhQoVYvDgwYwcOZI963/G2S09Z48fJmuWrIwePfqFxwwePBg/Pz9WrFhBZGQkc+fN\nIzoq6rn9JCaahg0bsnTpUj1HuaZpHwSd/LUUY8SIEVStWpUFCxYQEhJCxxZNad26NalTp37pMblz\n52bgwIFA7FDBKVO/p8Yn7ciUPRcAx37bxl8njzF8YD+d+DVN+2DooX6a9obu3btH2bLl+POvP/Es\nWZ6IR+H8cWQ/tWrVZtWqlaRK9fJr6aioKJRSeiIeTdMSjR7qp5nV7du3CQgIYNmyZYSEJJ8hb87O\nzuzfv49vR4/GyVLI4ubMvHnzXpn4AwMDqVq1GpaWltjY2ODXpAkXL15M2sA1TdP+Q9/5ayY1btw4\nBg8eTGRkJAA2trZMmTyZ9u3bmzmypHf69GmKFS+Oa3p3KjZoTuTjCLYsnYuV0UBQ0HFcXV+3Oram\nadqb03f+mlls2LCBfv36UaVJa6ZvPcb3vxyiZLW6fPbZZ/HmxE8pxo4di62DI0Pnr6Fa09bUbtWJ\nofNWcyc4mJkzZ5o7PE3TUjCd/DWT+eGHaeTy9OaTXoNxdEmDi1sG2g36loxZsjNjxgxzh5fkdv+2\nh6IVq2NtYxtX5uKWgXxFS/Pbnj1mjEzTtJROJ3/NZC5dvkS2vJ7xer0bDAYyf5SfixcvmTEy83Bx\ndiL4xj/xykSE4BvXcHF2NlNUmqZpOvlrJlSgQAFOHfwt3lj4yIhHnA08SMGCBcwYmXm0bt2aIzt/\nZd8vq4mJiSHqyRPWzZvG5XNnaNWqlbnD0zQtBdPj/DWT6fP55/xcujTffd6ej1t0IDrqCWvnfM+j\n8Pt0797d3OEluY4dO7Jr926+H9gd/4kjeRIZyf3Qe3z55Zf4+vq+vgJN07REopO/ZjLFixdn5cqV\ndO/eg1EdmwCQK1duNm7YwEcffWTm6JJeqlSpWLpkCd27dWPjxo1YWFjQqFEjPD09zR2apmkpnB7q\np5lcdHQ0p06dwmg0ki9fPj3znaZpWhJIyFA/feevmZzRaNR3t5qmae8x3eFP0zRN01IYnfw1TdM0\nLYXRyV/TNE3TUhid/DVN0zQthdHJXzObkJAQ+vfvT7bsOcjk7kGHDh24dCnlzQSoaZqW1HRvf80s\nwsPD8fEpz9/nz1P64/pYWduyYtUq1qxdy+FDh8icObO5Q9Q0TUu2dPLXzGLevHn88ccpRvlvInOu\nvADUatWJL/18GTt2LN9//72ZI9Q0TUu+9GN/zSw2b95M3iKl4hI/gKNLGkpWrcOmX341Y2SapmnJ\nn07+mlnY2NjwKPz+c+UPH9zHxsbGDBFpmqalHDr5a2bh5+fH36eC2LNxVVzZn0FHOLhlPc2aNjFj\nZJqmacmffuevmUW9evX4pHlzpg3uwfr507GyseGvE4GUKlWaXr16mTs8TdO0ZC1R7vyVUlmUUrOU\nUueVUg+VUn8ppYYqpSwS43zah8dgMLBwwQLWrVtHhVLFKJIvNwsWLGDHju3Y2dmZOzxN07RkLbHu\n/PMACvgM+BsoAMwCbIF+iXRO7QNjMBioVasWtWrVMncomqZpKUqiJH8R+RX4d5fti0qp8UAndPLX\nNE3TNLNKyg5/TsDdJDyfpmmapmkvkCTJXymVE+gGzEiK82mapmma9nIJeuyvlBoN9H/FLgLkFZE/\n/3VMJmATsFRE5rzJeXr37o2jo2O8smbNmtGsWbOEhKtpmqZpyVJAQAABAQHxykJDQ9/4eCUib76z\nUq6A62t2Oy8iUU/3zwjsAPaJSJs3qN8bOHr06FG8vb3fOC5N0zRNS+kCAwMpUqQIQBERCXzVvgl6\n7C8iwSLy52u2Z4k/E7GJ/zDQ9i3b8l7771VXcpUS2qnbmDzoNiYfKaGd5mxjYo3zzwjsBC4R27vf\nTSmVTimVLjHOZy4p4ZcTUkY7dRuTB93G5CMltNOcbUyscf5VgOxPtytPyxSxfQKMiXROTdM0TdPe\nQKLc+YvIfBEx/mcziIhO/JqmaZpmZnphH03TNE1LYd63hX2sAU6fPm3uON5IaGgogYGv7FCZLKSE\nduo2Jg+6jclHSminqdv4r9xp/bp9EzTUL7EppT4BFps7Dk3TNE37gDUXEf9X7fC+JX9XoBpwEYgw\nbzSapmma9kGxBrICv4pI8Kt2fK+Sv6ZpmqZpiU93+NM0TdO0FEYnf03TNE1LYXTy1zRN07QURid/\nTdM0TUthdPLXNE3TtBRGJ/93pJTKopSapZQ6r5R6qJT6Syk1VCllYe7YTE0pNVAptVcpFa6Uumvu\neExBKdVVKXVBKfVIKXVAKVXM3DGZklKqnFJqrVLqmlIqRilVx9wxmZpSaoBS6pBSKkwpdVMptUop\nldvccZmSUqqTUipIKRX6dNunlKpu7rgSk1Lqy6e/s9+ZOxZTUkp9/bRd/97+SOo4dPJ/d3mIXbTo\nMyAf0BvoBIwyZ1CJxAJYBkw3dyCmoJRqAkwAvga8gCDgV6VUGrMGZlp2wHGgC7ELayVH5YCpQAnA\nl9jf081KKRuzRmVaV4D+gDdQBNgOrFFK5TVrVInk6UV4B2L/JpOj34F0QPqnW9mkDkCP808ESqm+\nQCcRyWnuWBKDUqoVMFFEXMwdy7tQSh0ADopIz6dfK2I/ZKeIyFizBpcIlFIxQD0RWWvuWBLT04u3\nW4CPiOwxdzyJRSkVDPQVkbnmjsWUlFL2wFGgM/AVcExEPjdvVKajlPoaqCsi3uaMQ9/5Jw4nIFk8\nFk+unr6WKQJse1YmsVfCW4FS5opLMwknYp9yJMu/QaWUQSnVFLAF9ps7nkTwA7BORLabO5BElOvp\nq7i/lVKLlFIeSR3A+7awzwdPKZUT6AYkmyvVZCoNYARu/qf8JvBR0oejmcLTpzeTgD0ikuTvUROT\nUqoAscneGrgP1BeRM+aNyrSeXtQUBoqaO5ZEdABoDZwFMgBDgd1KqQIiEp5UQeg7/5dQSo1+QaeM\nf2/R/+1UpJTKBGwClorIHPNEnjBv005Ne49NI7bvTVNzB5IIzgCFgOLE9rtZoJTKY96QTEcp5U7s\nhVtzEXli7ngSi4j8KiI/i8jvIrIF+BhwBvySMg595/9y44HXvUs7/+x/lFIZie2Es0dEOiZmYCaW\noHYmI3eAaGI73fxbOuBG0oejvSul1PfEfpCWE5Hr5o7H1EQkiv//LR5TShUHehL7bjw5KAKkBQKf\nPsGB2KdzPkqpboCVJMNOaiISqpT6E0jSPmI6+b/E0xWRXrkq0jNP7/i3A4eBtokZl6klpJ3JiYg8\nUUodBSoDayHukXFlYIo5Y9MS7mnirwuUF5HL5o4niRgAK3MHYUJbgYL/KZsHnAa+TY6JH+I6OOYE\nFiTleXXyf0dP7/h3AheAfoDbs4tWEfnv++QP2tNOKS5AFsColCr09FvnkvJdlQl9B8x7ehFwiNhh\nmrbEfuAkC0opO2I/WJ7dSWV/+nO7KyJXzBeZ6SilpgHNgDpAuFLq2dOcUBFJFkuDK6W+IfaV4mXA\nAWgOlAeqmjMuU3r6GRKvn4ZSKhwIFpHT5onK9JRS44B1wCUgEzAMeAIEJGUcOvm/uypA9qfbsw9T\nRWxvY6O5gkokw4GW//o68Ol/KwK7kz6cdyMiy54OCxtO7OP+40A1Eblt3shMqiiwg9jfRyF2XgOA\n+XxgT6leoROxbdv5n/I2JPHdVCJyI/ZnlgEIBU4AVZN5j3hInnNTuAP+gCtwG9gDlHz6FDbJ6HH+\nmqZpmpbC6N7+mqZpmpbC6OSvaZqmaSmMTv6apmmalsLo5K9pmqZpKYxO/pqmaZqWwujkr2mapmkp\njE7+mqZpmpbC6OSvaZqmaSmMTv6apmmalsLo5K9pmqZpKYxO/pqmaZqWwvwPWz/Zf2526eYAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17d78ff27f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import SGDClassifier\n",
    "\n",
    "# Create two point arrays one for positive samples and one for negative samples\n",
    "n = 100\n",
    "\n",
    "Positive_mean = [3,3]\n",
    "Positive_cov = [[0.5, 0.0],[0.0, 0.5]]\n",
    "Positive_points = np.random.multivariate_normal(Positive_mean, Positive_cov, n)\n",
    "\n",
    "Negative_mean = [0,0]\n",
    "Negative_cov = [[0.5, 0.0],[0.0, 0.5]]\n",
    "Negative_points = np.random.multivariate_normal(Negative_mean, Negative_cov, n)\n",
    "\n",
    "# Merge the two arrays into one\n",
    "points = np.random.multivariate_normal(Negative_mean, Negative_cov, n*2)\n",
    "for i in range(len(points)):\n",
    "    if i < n:\n",
    "        points[i] = Positive_points[i]\n",
    "    else:\n",
    "        points[i] = Negative_points[i-n]\n",
    "\n",
    "# generate the target array\n",
    "targets = np.ones(n*2)\n",
    "for i in range(len(targets)):\n",
    "    if i < n:\n",
    "        targets[i] = 1\n",
    "    else:\n",
    "        targets[i] = 0\n",
    "\n",
    "# fit the model\n",
    "clf = SGDClassifier(loss=\"hinge\", alpha=0.01, n_iter=200, fit_intercept=True)\n",
    "clf.fit(points, targets)\n",
    "\n",
    "\n",
    "# plot the line, the points, and the nearest vectors to the plane\n",
    "xx = np.linspace(-1, 5, 10)\n",
    "yy = np.linspace(-1, 5, 10)\n",
    "\n",
    "X1, X2 = np.meshgrid(xx, yy)\n",
    "Z = np.empty(X1.shape)\n",
    "for (i, j), val in np.ndenumerate(X1):\n",
    "    x1 = val\n",
    "    x2 = X2[i, j]\n",
    "    p = clf.decision_function([[x1, x2]])\n",
    "    Z[i, j] = p[0]\n",
    "\n",
    "plt.contour(X1, X2, Z, levels=[0.0], colors='k', linestyles='solid')\n",
    "plt.scatter(points[:, 0], points[:, 1], c=targets, cmap=plt.cm.Paired)\n",
    "\n",
    "plt.axis('tight')\n",
    "plt.show()\n"
   ]
  }
 ],
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